The phrase that you have mentioned (vid sidan av den briljanta eliten) might be seen as:

the ones who are set apart as special due to their intelligence
the intelligent ones of the class that is set apart

This phrase could also be meant sarcastically which would be even more biting than what you noted earlier.

It would be nice to have someone who speaks Swedish and English fluently comment on the semantics of that sentence. I have tried to fill in shades of meaning by using German, but that does not always work very well - idioms can be difficult: n.b., the well-known phrase 'lost in translation'. However, if Swedish is very similar to German and if I am not misunderstanding the phrase or the intention of the author, the phrase may be read as an acknowledgement of the fact that there are some exceptionally well-educated people in the USA and not as a praising of the wealthy 1% in the USA.

I am not quite interested to the point of emailing the author and asking her directly about the meaning of her article (pun intended), but maybe you would???